In a large heavy-bottomed pot, saute the onion and garlic in the butter and olive oil over medium-high heat until onion is soft and translucent. Add the sun-dried tomatoes and fresh tomato, along with the broth and thyme. Simmer briefly to cook fresh tomato.

Remove soup from heat and let cool slightly. Add half of mixture to a blender or food processor; puree (be sure and place a towel over lid to avoid hot, spurting liquid). Return soup to pot and whisk in the cream. Add the salt and pepper to taste.

Divide the cheese between the 4 rolls. Place them in a preheated panini press and cook until bread is golden and cheese is melted.